Zhi's Modest List of
Publications
Papers
Published in Journals and Books
- Hao Liang and Sizhuo
Yan and Jianting Yang
and Lihong
Zhi
The non-Archimedean Nirgendsnegativsemidefinitheitsstellensatz is not true Isreal Journal of Mathematics (to appear 2024).
LYYZ2023.pdf - Nan Li and Zijia
Li and Zhi-Hong Yang
and Lihong
Zhi
The integral closure of a primary ideal is not always primary
Journal of Symbolic Computation, 125,2024
LLYZ2024.pdf - Kisun Lee and Nan
Li and Lihong
Zhi
Two-step Newton¡¯s method for deflation-one singular zeros of analytic systems
Journal of Symbolic Computation, 123,2024
LLZ2024.pdf - Feng Guo and Sizhuo
Yan and Lihong
Zhi
Extensions of S-Lemma for Noncommutative Polynomials
Journal of Operator Theory (to appear 2023)
GYZ203.pdf - Nan Li and Lihong
Zhi
Improved Two-Step Newton's Method for Computing Simple Multiple Zeros of Polynomial Systems
Numerical Algorithms, 91:19-50, 2022
LiZhi2022.pdf - Mohab
Safey El Din and Zhihong
Yang and Lihong
Zhi
Computing Real Radicals and S-radicals of Polynomial Systems
Journal of Symbolic Computation, 102:259-278, 2021.
SafeyYangZhi2019.pdf - Nan Li and Lihong Zhi
Sybmolic-numeric Method for Computing Isolated Singular Solutions
Scientia Sinica Mathematica, 51(1):17-42, 2021.
LiZhi2021.pdf - Shmuel
Friedland and Jingtong
Ge and Lihong Zhi
Quantum Strassen Theorem
Infinite Dimensional Analysis, Quantum Probability and Related Topics 23(3):1-29, 2020.
FGZ2020.pdf - Zhiwei
Hao and Wenrong Jiang
and Nan Li and Lihong
Zhi
On Isolation of Simple Multiple Zeros and Clusters of Zeros of Polynomial Systems
Mathematics of Computation, 89(322):879-909, 2020.
HaoJiangLiZhi2020.pdf - Chu
Wang and Lihong
Zhi
Lifts of Non-compact Convex Sets and Cone Factorizations
Journal of Systems Science and Complexity 33:1632-1655, 2020.
WangZhi2019.pdf - Chu
Wang and Zhihong
Yang and Lihong
Zhi
Global Optimization of Polynomials over Real Algebraic Sets
Journal of Systems Science and Complexity 32:158-184, 2019.
WangYangZhi2019.pdf - Yue
Ma and Chu Wang and Lihong Zhi
A Certificate for Semidefinite Relaxations in Computing Positive-Dimensional Real Radical Ideals
Journal of Symbolic Computation, 72:1-20, 2016.
MaWangZhi2016.pdf - Feng
Guo and Chu
Wang and Lihong
Zhi
Semidefinite Representations of Non-compact Convex Sets
SIAM Journal on Optimization, 25(1):377-395, 2015.
GuoWangZhi2015.pdf - Nan
Li and Lihong
Zhi
Verified Error Bounds for Isolated Singular Solutions of Polynomial Systems
SIAM Journal on Numerical Analysis, 52(4):1623-1640, 2014.
VMR.pdf - Zijia Li and Lihong Zhi
Computing the Nearest Singular Univariate Polynomials with Given Root Multiplicities
Theoretical Computer Science 479:163-173, 2013.
LiZijiaZhiTCS.pdf - Nan
Li and Lihong
Zhi
Verified Error Bounds for Isolated Singular Solutions of Polynomial Systems: Case of Breadth One
Theoretical Computer Science 479:150-162, 2013.
LiZhiTCS.pdf - Nan
Li and Lihong
Zhi
Computing isolated singular solutions of polynomial systems: case of breadth one
SIAM Journal on Numerical Analysis, 50(1):354-372, 2012.
LiZhi2011revised.pdf - Aurélien Greuet , Feng
Guo, Mohab
Safey El Din and Lihong
Zhi
Global optimization of polynomials restricted to a smooth variety using sums of squares
Journal of Symbolic Computation, 47:503-518, 2012.
Preliminary version sos_vcg_final.pdf - Mohab Safey El Din and Lihong Zhi
Computing rational points in convex semi-algebraic sets and sums of squares decompositions
SIAM Journal on Optimization, 20(6):2876-2889, 2010.
convex_sas.pdf - Nan
Li and Lihong
Zhi
Computing the multiplicity structure of an isolated singular solution: case of breadth one
Journal of Symbolic Computation, 47(6):700-710, 2012.
finalversionLIZHI.pdf - Erich
Kaltofen, Bin Li, Zhengfeng
Yang, and Lihong
Zhi
Exact certification in global polynomial optimization via sums-of-squares of rational functions with rational coefficients
Journal of Symbolic Computation, 47(1):1-15, 2012.
KLYZ09.pdf - Xiaoli Wu and Lihong Zhi
Computing the multiplicity structure from geometric involutive form
Journal of Symbolic Computation, 47(3):227-238, 2012.
jsc_zhiwu.pdf - Bin
Li, Jiawang Nie,and Lihong Zhi
Approximate GCDs of polynomials and sparse SOS relaxations.
Theoretical Computer Science, 409(2) pp.200-210, 2008.
LNZTCS08.pdf - Greg
Reid and Lihong
Zhi
Solving polynomials systems via symbolic-numeric eliminational method.
Journal of Symbolic Computation, 44 pp.280-291, 2009.
ReidZhiJSC08.pdf - Erich
Kaltofen, John P. May, Zhengfeng Yang,
and Lihong Zhi
Approximate factorization of multivariate polynomials using singular value decomposition.
Journal of Symbolic Computation, 43(5) pp.359-376, 2008.
KMYZJSC08.pdf
- Bingyu Li, Zhuojun Liu, and Lihong Zhi
A Structured Rank-revealing Method for Sylvester Matrix
Journal of Computational and Applied Mathematics,213 pp.212-223, 2008
llzcam08.pdf - Bingyu Li, Zhuojun Liu, and Lihong Zhi
AFast Algorithm for Solving the Sylvester Structured TotalLeast Squares Problem
Signal Processing, 87 (2007) pp.2313-2319.
llzsp07.pdf - Dongxia Sun and Lihong Zhi
Structured Low Rank Approximation of a Bezout Matrix
Mathematics in Computer Science, 2 (2007) pp.427-437.
SunZhiMCS07.pdf - Bingyu Li, Zhengfeng Yang, and Lihong Zhi
Fast Low Rank Approximation of a Sylvester Matrix by Structure Total Least Norm
Journal of Japan Society for Symbolic and Algebraic Computation, 11(3,4) (2005) pp.165-174.
lyzjssac05.ps - Robert
M. Corless, Stephen M. Watt, and Lihong Zhi
QR Factoring to Compute the GCD of Univariate Approximate Polynomials
IEEE Transactions on Signal Processing, 52(12) pp.3394-3402, 2004.
QRGCD.pdf - Lihong Zhi, Matu-Tarow Noda, Hiroshi Kai, and Wenda
Wu
Hybrid Method for Computing the Nearest Singular Polynomials
Japan Journal of Industrial and Applied Mathematics, 21(2) pp.149-162, June 2004.
znkwjjiam04.pdf - Lihong Zhi
Hybrid ComputationLectures on Computer Algebra, (Ed. Dongming Wang, Lu Yang, Lihong Zhi, etc.), Tsing Hua Press, 2003.
hybrid.pdf - Lihong Zhi
Algebraic Factorization and GCD Computation
Mathematics Mechanization and Applications, (Ed. Xiao-Shan Gao and Dongming Wang), Academic Press, 2000, pp 325-342.
mmfac.pdf - K.
Shiraishi H., Lihong Zhi, and Matu-Tarow Noda
Implement of Wu's Method in Risa/Asir
Journal of Japan Society for Symbolic and Algebraic Computation, 7(3) (1999) pp.41-42(abstract). - H.
Minaguchi, Lihong Zhi
, Hiroshi Kai and Matu-Tarow Noda
Apply General Inverse of Matrix to Compute Nearest Singular Polynomials
Journal of Japan Society for Symbolic and Algebraic Computation, 7(3) (1999) pp.29-30(abstract). - Lihong Zhi and Zhuojun Liu
The P-irreducibility of Binding Polynomials
An International Journal of Computers & Mathematics with Applications, 38(2) (1999) pp.1-10.
pirr.pdf - Lihong Zhi and Wenda Wu
Nearest Singular Polynomials
Journal of Symbolic Computation, 26(6) pp.667-676, December 1998.
nsp.pdf - Lihong Zhi
An Optimal Method for Algebraic Factoring
Journal of Computer Science and Technology, 12 pp. 1-9, January 1997.
opfac.pdf
Papers
Published in Conference Proceedings
- Sizhuo Yan, Jianting Yang,
Tianshi Yu and Lihong
Zhi
A Characterization of Perfect Strategies for Mirror Games
In ISSAC'2023 Proc. 2023 Internat. Symp. Symbolic Algebraic Comput.
YYYZ2023.pdf - Mohab Safey El Din, Zhi-Hong Yang, and Lihong Zhi
On the complexity of computing real radicals of polynomial
In ISSAC'2018 Proc. 2018 Internat. Symp. Symbolic Algebraic Comput.
SafeyYangZhi2018.pdf - Jean-Guillaume Dumas, Erich L. Kaltofen,
Gilles Villard and Lihong
Zhi
Polynomial Time Interactive Proofs for Linear Algebra with Exponential Matrix Dimensions and Scalars Given by Polynomial Time Circuits
In ISSAC'2017 Proc. 2017 Internat. Symp. Symbolic Algebraic Comput.
DKVZ2017.pdf - Lihong Zhi
Computing Multiple Zeros of Polynomial Systems: Case of Breadth One
In CASC'2017 . International Workshop on Computer Algebra in Scientific Computing.
Zhi2017.pdf - Zhiwei Hao, Erich L.
Kaltofen, and Lihong
Zhi
Numerical sparsity determination and early termination
In ISSAC'2016 Proc. 2016 Internat. Symp. Symbolic Algebraic Comput.
HKZ2016.pdf - Feng
Guo, Mohab Safey
El Din, Chu Wang, and Lihong
Zhi
Optimizing a parameteric linear function over a non-compact real algebraic variety
In ISSAC'2015 Proc. 2015 Internat. Symp. Symbolic Algebraic Comput.
GSWZ2015.pdf - Feng
Guo, Chu
Wang, and Lihong
Zhi
Optimizing a Linear Function over a Noncompact Real Algebraic Variety
In SNC'2014 Proc. SNC Internat. Symp. Symbolic-Numeric Computation.
GWZ2014SNC.pdf - Qingdong Guo, Mohab Safey
El Din, and Lihong
Zhi
Computing rational solutions of linear matrix inequalities
In ISSAC'2013 Proc. 2013 Internat. Symp. Symbolic Algebraic Comput.
GuoSafeyZhiISSAC2013.pdf - Zhengfeng Yang, Lihong Zhi, and Yijun
Zhu
Verfied error bounds for real solutions of positive-dimensional polynomial systems
In ISSAC'2013 Proc. 2013 Internat. Symp. Symbolic Algebraic Comput.
YangZhiZhuISSAC2013.pdf
- Feng Guo, Erich Kaltofen,
and Lihong Zhi
Certificates of impossibility of Hilbert-Artin representations of a given degree for definite polynomials and functions
In ISSAC'2012 Proc. 2012 Internat. Symp. Symbolic Algebraic Comput. pp. 195-202
URL: http://arxiv.org/abs/1203.0253.
- Yue
Ma and Lihong
Zhi
Computing Real Solutions of Polynomial Systems via Low-Rank Moment Matrix Completion In ISSAC'2012 Proc. 2012 Internat. Symp. Symbolic Algebraic Comput. pp. 249-256
MaZhiISSAC2012.pdf - Yue
Ma and Lihong
Zhi
The Minimum-Rank Gram Matrix Completion via Modified Fixed Point Continuation Method
In ISSAC'2011 Proc. 2011 Internat. Symp. Symbolic Algebraic Comput. pp. 241-248
MaZhiISSAC2011.pdf
- Sharon Hutton, Erich Kaltofen, and Lihong
Zhi
Computing the radius of positive semidefiniteness of a multivariate real polynomial via a dual of seidenberg¡¯s method
In ISSAC'2010 Proc. 2010 Internat. Symp. Symbolic Algebraic Comput. pp. 227-234
p227-hutton.pdf
- Zijia Li, Zhengfeng
Yang, and Lihong
Zhi
Blind image deconvolution via fast approximate GCD
In ISSAC'2010 Proc. 2010 Internat. Symp. Symbolic Algebraic Comput. pp. 155-162
55_paper.pdf - Feng
Guo, Mohab Safey
El Din, and Lihong
Zhi
Global optimization of polynomials using generalized critical values and sums of squares
In ISSAC'2010 Proc. 2010 Internat. Symp. Symbolic Algebraic Comput. pp. 107-114
p107-guo.pdf - Xiaoli Wu and Lihong Zhi
Computing the multiplicity structure from geometric involutive form
In ISSAC'08 Proc. 2008 Internat. Symp. Symbolic Algebraic Comput. pp. 325-332
WuZhiISS08.pdf - Erich
Kaltofen, Bin Li, Zhengfeng
Yang, and Lihong
Zhi
Exact certification of global optimality of approximate factorizations via rationalizing sums-of-squares with floating point scalars.
In ISSAC'08 Proc. 2008 Internat. Symp. Symbolic Algebraic Comput. pp. 155-163
KLYZISS08.pdf - Erich Kaltofen,
Zhengfeng Yang, and Lihong
Zhi
On Probabilistic Analysis of Randomization in Hybrid Symbolic-Numeric Algorithms
In Proc. 2007 Internat. Workshop on Symbolic-NumericComput. pp. 11-17
KYZsnc07.pdf - Erich Kaltofen,
Bin Li, Kartik Sivaramakrishnan,
Zhengfeng Yang, and Lihong
Zhi
Lower Bounds for Approximate Factorizations via Semidefinite Programming(extended abstract)
In Proc. 2007 Internat. Workshop on Symbolic-NumericComput. pp. 203-204
KLSYZsnc07.pdf - Bin Li, Jiawang
Nie, and Lihong
Zhi
Approximate GCDs of Polynomials and SOS Relaxation (extended abstract)
In Proc. 2007 Internat. Workshop on Symbolic-Numeric Comput. pp. 205-206
lnzsnc07.pdf - Lihong Zhi
Numerical Optimization in Hybrid Symbolic-numeric Computation (extended abstract)
In Proc. 2007 Internat. Workshop on Symbolic-NumericComput.pp. 33-35
zhisnc07.pdf - Erich
Kaltofen and Lihong Zhi
Hybrid Symbolic-numeric Computation
In ISSAC'06 Proc. 2006 Internat. Symp. Symbolic Algebraic Comput. pp. 7
KZiss06.pdf - Erich
Kaltofen, Zhengfeng
Yang, and Lihong
Zhi
Approximate Greatest Common Divisors of Several Polynomials with Linearly Constrained Coefficients and Singular Polynomials
In ISSAC'06 Proc. 2006 Internat. Symp. Symbolic Algebraic Comput. pp. 169-176
KYZiss06.pdf - Bingyu Li , Zhuojun Liu, and Lihong Zhi
A Structured Rank-revealing Method for Sylvester Matrix
Conference on Applications of Computer Algebra, July 31-August 3, 2005 - Bingyu Li , Zhuojun Liu, and Lihong Zhi
Fast Low Rank Approximation of a Sylvester Matrix
In Dongming Wang and Lihong Zhi, editors, International Workshop on Symbolic-Numeric Computation SNC 2005 Proceedings, pp. 202-208, 2005
LLZsnc05.ps - Erich
Kaltofen, Zhengfeng
Yang, and Lihong
Zhi
Structured Low Rank Approximation of a Sylvester Matrix
In Dongming Wang and Lihong Zhi, editors, International Workshop on Symbolic-Numeric Computation SNC 2005 Proceedings, pp. 188-201, 2005
KYZsnc05.ps - Greg
Reid and Lihong
Zhi
Solving Nonlinear Polynomial System via Symbolic-Numeric Elimination Method
Proceedings of international conference on polynomial system solving£¬pp. 50-53£¬ 2004
rzicpss04.pdf - Greg
Reid, Jianliang Tang, Jianping
Yu, and Lihong
Zhi
Hybrid method for solving new pose estimation equation system
Proceedings of the 2004 International Workshop on Computer and Geometric Algebra with Applications, LNCS 3519, H. Li et al. (eds), Springer Berlin Heidelberg, pp.46-57, 2005.
rtyz04.pdf - Shuhong Gao,
Erich Kaltofen, John P. May, Zhengfeng Yang,
and Lihong Zhi
Approximate factorization of multivariate polynomials via differential equations.
Proceedings of the 2004 International Symposium on Symbolic and Algebraic Computation, pp. 167-174, 2004. ACM SIGSAM's ISSAC 2004 Distinguished Student Author Award (May and Yang).
GKMYZ04.pdf - Joe
Bonasia, Francois Lemaire,
Greg Reid, Robin Scott, and Lihong Zhi
Determination of approximate symmetries of differential equations
In Gomez-Ullate (ed.), CRM Proceedings and Lecture Notes 39: 233-249, Amer. Math. Soc, 2004.
ApproxSym.pdf - Lihong Zhi
Displacement Structure in Computing the Approximate GCD of Univariate Polynomials
Mathematics, pp.288-298, W.Sit and Z. Li(eds), World Scientific (Lecture Notes Series on Computing) 2003.
displacement.pdf - Greg
Reid, Jianliang Tang, and Lihong Zhi
A Complete Symoblic-Numeric Linear Method for Camera Pose Determination
Proceedings of the 2003 International Symposium on Symbolic and Algebraic Computation, pp. 215-223, 2003.
trzissac03.pdf - Lihong Zhi, M.-T Noda, and K.
Li
On the construction of PSE for GCD Computation
Proceedings of the Asian Symposium on Computer Mathematics, pp.76-81, World Scientific (Lecture Notes Series on Computing) 2001. - Kai
Li, Lihong
Zhi, and Matu-Tarow
Noda
Solving Approximate GCD of Multivariate Polynomials By Maple/Matlab/C Combination
Proceedings of the Asian Technology Conference in Mathematics, pp.492-499, Chiangmai,
znlatcm00.pdf - Lihong Zhi and M.-T.
Noda
Approximate GCD of Multivariate Polynomials
Proceedings of the Asian Symposium on Computer Mathematics, pp.9-18, Chiangmai,
znascm00.pdf - Yuzhen
Huang, H.J.Stetter , Wenda Wu,
and Lihong Zhi
Pseudofactors of Multivariate Polynomials
Proceedings of the 2000 International Symposium on Symoblic and Algebraic Compuation, pp.161-168.
HSWZISS00.ps - Lihong Zhi , Y. Notake, H. Kai, and M.-T. Noda
Hybrid Method for Solving Polynomial Equations
Proceedings of the Asian Technology Conference in Mathematics, pp.492-501,
atcm99.pdf - Lihong Zhi and Wenda Wu
Nearest Singular Polynomials I
Proceedings of the Asian Technology Conference in Mathematics, pp.323-332, Tsukuba, - Dongming Wang and Lihong Zhi
Algebraic Factorization Applied to Geometric Problems
Proceedings of the Asian Symposium on Computer Mathematics, pp.23-36, Lan Zhou,
zwfac.pdf - Lihong Zhi and Wenda Wu
A Note on Small Perturbations to Polynomials(abstract)
Proceedings of the Asian Technology Conference in Mathematics, - Kai
Huang, Dingkang Wang, and Lihong Zhi
Wu method and its Applications (abstract)
Proceedings of the Asian Technology Conference in Mathematics,
hwzatcm97.pdf - Dingkang Wang and Lihong Zhi
Software Development in MMRC
Proceedings of the Asian Technology Conference in
sdmmrc.pdf
Posters
- R.
Corless, S. Watt, and Lihong Zhi
QR Factorization for Computing Approximate GCD
The 2002 International Symposium on Symbolic and Algebraic Computation, 2002. - Iyad A. Ajwa and Lihong Zhi
CharSets: An Efficient Implementation of the Characteristic Sets Method
The Fifth Annual East Coast Computer Algebra Day, ECCAD '98, United States Naval Academy, Annapolis, Maryland, April 25, 1998.
Technical
Reports
Dissertation
- Lihong Zhi
Polynomial Factorization over Algebraic Fields and its Applications
Ph.D. Dissertation,
Go Back to Zhi's Home